Nuprl Lemma : geo-out_inversion
∀e:BasicGeometry. ∀a,b,c:Point. (out(a bc) ⇒ out(a cb))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
not: ¬A,
cand: A c∧ B,
and: P ∧ Q,
geo-out: out(p ab),
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
geo-out_wf,
geo-between_wf,
not_wf
Rules used in proof :
independent_isectElimination,
instantiate,
sqequalRule,
because_Cache,
applyEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
productEquality,
independent_functionElimination,
independent_pairFormation,
hypothesis,
cut,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:Point. (out(a bc) {}\mRightarrow{} out(a cb))
Date html generated:
2017_10_02-PM-06_26_19
Last ObjectModification:
2017_08_05-PM-04_19_43
Theory : euclidean!plane!geometry
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